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Course10310111149 lectures

Advanced Numerical Analysis

Prof. Sachin C. Patwardhan · IIT Bombay

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Lectures

Advanced Numerical Analysis

  1. Lecture 1: Introduction and Overview Video
  2. Lecture -2 Fundamentals of Vector Spaces Video
  3. Lecture 3 : Basic Dimension and Sub-space of a Vector Space Video
  4. Lecture 4 : Introduction to Normed Vector Spaces Video
  5. Lecture 5 : Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces Video
  6. Lecture 6 : Introduction to Inner Product Spaces Video
  7. Lecture 7 : Cauchy Schwaz Inequality and Orthogonal Sets Video
  8. Lecture 8 : Gram-Schmidt Process and Generation of Orthogonal Sets Video
  9. Lecture 9 : Problem Discretization Using Appropriation Theory Video
  10. Lecture 10 : Weierstrass Theorem and Polynomial Approximation Video
  11. Lecture 11 : Taylor Series Approximation and Newton's Method Video
  12. Lecture 12 : Solving ODE - BVPs Using Firute Difference Method Video
  13. Lecture 13 :Solving ODE - BVPs and PDEs Using Finite Difference Method Video
  14. Lecture 14 : Finite Difference Method (contd.) and Polynomial Interpolations Video
  15. Lecture 15 : Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving ODE -BVPs Video
  16. Lecture 16 : Orthogonal Collocations Method for Solving ODE - BVPs and PDEs Video
  17. Lecture 17 :Least Square Approximations, Necessary and Sufficient Conditions for Unconstrained Optimization Video
  18. Lecture 18 : Least Square Approximations :Necessary and Sufficient Conditions for Unconstrained Optimization Least Square Approximations ( contd..) Video
  19. Lecture 19 :Linear Least Square Estimation and Geometric Interpretation of the Least Square Solution Video
  20. Lecture 20 : Geometric Interpretation of the Least Square Solution (Contd.) and Projection Theorem in a Hilbert Spaces Video
  21. Lecture 21 : Projection Theorem in a Hilbert Spaces (Contd.) and Approximation Using Orthogonal Basis Video
  22. Lecture 22 :Discretization of ODE-BVP using Least Square Approximation Video
  23. Lecture 23 : Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method Video
  24. Lecture 24 : Model Parameter Estimation using Gauss-Newton Method Video
  25. Lecture 25 : Solving Linear Algebraic Equations and Methods of Sparse Linear Systems Video
  26. Lecture 26 : Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving Linear Algebraic Equations Video
  27. Lecture 27 : Iterative Methods for Solving Linear Algebraic Equations Video
  28. Lecture 28 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Eigenvalues Video
  29. Lecture 29 :Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Matrix Norms Video
  30. Lecture 30 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Matrix Norms (Contd.) Video
  31. Lecture 31 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis (Contd.) Video
  32. Lecture 32 :Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method Video
  33. Lecture 33 : Conjugate Gradient Method, Matrix Conditioning and Solutions of Linear Algebraic Equations Video
  34. Lecture 34 : Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.) Video
  35. Lecture 35 : Matrix Conditioning (Contd.) and Solving Nonlinear Algebraic Equations Video
  36. Lecture 36 : Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton's Method Video
  37. Lecture 37 : Solving Nonlinear Algebraic Equations: Optimization Based Methods Video
  38. Lecture 38 : Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis of Iterative Solution Techniques Video
  39. Lecture 39 : Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis (Contd.) and Solving ODE-IVPs Video
  40. Lecture 40 :Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) : Basic Concepts Video
  41. Lecture 41 :Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) : Runge Kutta Methods Video
  42. Lecture 42 :Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods Video
  43. Lecture 43 :Solving ODE-IVPs : Generalized Formulation of Multi-step Methods Video
  44. Lecture 44 : Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method Video
  45. Lecture 45 : Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis of Solution Schemes Video
  46. Lecture 46 : Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.) Video
  47. Lecture 47 :Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.) and Solving ODE-BVP using Single Shooting Method Video
  48. Lecture 48 : Methods for Solving System of Differential Algebraic Equations Video
  49. Lecture 49 : Methods for Solving System of Differential Algebraic Equations (contd.) and Concluding Remarks Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Chemical Engineering
Teacher
Prof. Sachin C. Patwardhan
Level
Undergraduate
Language
English
Subjects
Chemistry, Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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